(Reuters) - As protests sweep the developing world and Europe struggles through an austerity hangover, China and the U.S., relative to their peers, look like the best in class.

They are both comfortable with their modest economic growth rates compared to their norms of the past decade, and are insulated from the kind of social unrest we are seeing in Egypt, Turkey or Brazil. But both countries have a deeper intractable challenge that will, in the longer-term, get worse. What's interesting is that they're the inverse of each other. In the U.S., wealth and private sector interests capture the political system. In China, politicians capture the private sector and the wealth that comes with it.

The U.S.'s struggles with lobbying, pork-barrel spending, and the corporate sector's general overlord status in Washington are well documented. Campaign finance reform is long past. Corporate personhood is well-entrenched. Super PACs are ascendant. A representative democracy is being crowded out by a capitalist one.

The cycle is hard to break. Politicians' interests become aligned with those of the corporations that help them get elected. But even more troubling is that so many American politicians are gearing up to join the lobbying machine after they retire from government. In 1974, 3.0 percent of retiring members of Congress became lobbyists. Today, the figure stands at 50 percent of senators, and 42 percent of the House.

China has a related but different problem. Its politicians control too much of the money themselves. Politicians and elites in China enrich themselves, their friends, and their families by managing and siphoning China Inc., China's state capitalist enterprise. Chinese industry is controlled by the state, and thus it is the property of the people who run the state. Last year, state-owned enterprises and affiliated businesses accounted for over half of Chinese economic output and employment. There were 70 mainland Chinese companies on the 2012 Fortune Global 500 list; 65 of those were state-owned.

As an example, look no lower than China's People's Congress. The United States' House of Representatives and Senate has no billionaires. China's parliament has 83. According to Bloomberg, "The richest 70 members of China's legislature added more to their wealth last year than the combined net worth of all 535 members of the U.S. Congress, the president and his Cabinet, and the nine Supreme Court justices." If you're part of the state, state capitalism is the best, even if the system is centralized, corrupt and calcified.

That is where China's trouble is: its inability to create a robust industrial sector that can spread the wealth. It is leading to severe income inequality. Reliable financial metrics can be hard to come by in China, but a survey by a Chinese university suggests the wealth gap is now well above the world's average and "10 percent of Chinese households held up to 57 percent of all disposable income."

Income inequality is of course a problem in the U.S. as well. Just this week, the New York Times reported on how medical and pharmaceutical companies have ensured that giving birth in America is costlier than anywhere else in the world. Yet the country is still sufficiently stable, resilient and wealthy. America's poor people are still well-to-do from a global perspective. China's are less so. One in ten Chinese live on the equivalent of $1.50 a day or less. In other emerging markets this has, and is, leading to mass protest. But in China what can be done to placate the masses when it comes to corruption?

Xi Jinping is very popular, and he's eager to make a show of addressing political corruption. He announced a fight against the "four forms of decadence" — formalism, bureaucracy, hedonism and extravagance. The party leadership may be priming itself for a purge, locating local and midlevel officials that are low-hanging fruit: people they can make a public example of without impacting the top of the pyramid.

As for the wealthiest, they are undergoing a PR campaign of sorts, trying to display more modesty. China's foreign minister just traded in his Audi for the same domestic model that Mao used to drive around in. Make no mistake these actions are largely cosmetic. They mitigate public dissent in the short-term, but they do not get at the root of the problem. Why is that? China's leaders cannot fundamentally go after the problem because the problem is them.

And so we are left with a world in which the two strongest countries offer mirrored visions of what it takes to get to the top. In the U.S., the biggest danger of the capitalist system is that the private sector captures the state. In China, the biggest problem with state capitalism is that the state has already captured the private sector.

This is not to say that China is doomed. It, like the U.S., is in a powerful position despite its fundamental inefficiencies. The world's two largest economies are humming along at modest clips and economic growth has a way of shading over entrenched structural concerns. Both the United States and China are positioned to kick the can down the road for the foreseeable future, but eventually they will have to face their biggest issues. And it's best that they do so sooner rather than later.

It is fascinating that the two countries with the largest economies have inverse imperfections. But will they have inverse fates?

(This column is based on a transcribed phone interview with Bremmer. Ian Bremmer is the president of Eurasia Group, the leading global political risk research and consulting firm. Bremmer created Wall Street's first global political risk index, and has authored several books, including the national bestseller, The End of the Free Market: Who Wins the War Between States and Corporations?, which details the new global phenomenon of state capitalism and its geopolitical implications. He has a PhD in political science from Stanford University (1994), and was the youngest-ever national fellow at the Hoover Institution.)